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2_d_riemann.py
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2_d_riemann.py
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import numpy as np
import scipy.optimize as opt
class PatchInit:
def __init__(self,t,bp,bs=None,fs=None):
self.type = t
self.bounding_points = bp
self.boundary_surface = bs
self.flow_state = fs
class BoundsInit:
def __init__(self,lf,rf,bof,tf,baf,ff):
self.left_face = lf
self.right_face = rf
self.bottom_face = bof
self.top_face = tf
self.back_face = baf
self.front_face = ff
def init():
left_face_init = []
right_face_init = []
top_face_init = []
bottom_face_init = []
back_face_init = []
front_face_init = []
# inflow_condition = inflow_generator()
initial_conds = initial_condition()
left_face_init.append(
PatchInit('Inflow',
((0.0,0.0,0.0),(0.0,0.0,1.0),(0.0,1.0,1.0),(0.0,1.0,0.0)),
'f = x',
initial_conds[:,0,:,:]))
right_face_init.append(
PatchInit('Outflow',
((.6,-1.0,-1.0),(.6,2.0,-1.0),(.6,2.0,2.0),(.6,-1.0,2.0)),
'f = -x+.6',
None))
bottom_face_init.append(
PatchInit('Transmissive',
((-1.0,0.0,0.0),(1.0,0.0,0.0),(1.0,0.0,1.0),(-1.0,0.0,1.0))))
top_face_init.append(
PatchInit('Transmissive',
((-1.0,1.0,0.0),(0.8,1.0,0.0),(0.8,1.0,1.0),(-1.0,1.0,1.0))))
back_face_init.append(
PatchInit('Transmissive',
((-1.0,0.0,0.0),(0.8,0.0,0.0),(0.8,1.0,0.0),(-1.0,1.0,0.0))))
front_face_init.append(
PatchInit('Transmissive',
((-1.0,0.0,1.0),(0.8,0.0,1.0),(0.8,1.0,1.0),(-1.0,1.0,1.0))))
bounds_init = BoundsInit(lf=left_face_init,rf=right_face_init,
bof=bottom_face_init,tf=top_face_init,
baf=back_face_init,ff=front_face_init)
exact_sol_kwargs = {'pR':.25,'dR':.5,'MR':7,'alphaR':np.pi*.5,
'pL':1.,'dL':1.,'ML':2.4,'alphaL':np.pi*.5,
'gamma':1.4}
exact_solution_obj = SteadyRiemannSolution(**exact_sol_kwargs)
exact_solution = lambda t,indxi,indeta,indzeta :(
np.array(
list(exact_solution_obj(
initial_conds[17,indxi,indeta,indzeta],
initial_conds[18,indxi,indeta,indzeta]-.5))
+list(initial_conds[5:,indxi,indeta,indzeta])
)
)
solver_options = np.zeros(300)
solver_options[0] = 1
solver_options[100] = 1
solver_options[101] = 1
solver_options[102] = 0
solver_options[103] = 0
stream_options = {
'solver_type':'euler',
'boundary_layers':False,
'multistream':False,
'solver_options':solver_options,
'manufactured':False,
'source_funcs':None,
'exact_sol_func':exact_solution}
return bounds_init, initial_conds, stream_options
def initial_condition():
nx,ny,nz = 30,50,1
xmin,xmax = 0.,.6
ymin,ymax = -.5,.5
zmin,zmax = 0.,0.
dx,dy,dz = (xmax-xmin)/(nx),(ymax-ymin)/(ny),1
inputs = np.zeros((21,nx,ny,nz))
inputs[0,:,:,:] = 1.
inputs[0,:,ny/2:,:] = .25
inputs[1,:,:,:] = 1.
inputs[1,:,ny/2:,:] = .5
inputs[2,:,:,:] = 2.4*np.sqrt(1.4)
inputs[2,:,ny/2:,:] = 7*np.sqrt(.25/.5*1.4)
inputs[5,:,:,:] = dx
inputs[9,:,:,:] = dy
inputs[13,:,:,:] = dz
for inda in range(ny):
for indb in range(nx):
inputs[17,indb,inda,0] = (indb+.5)*dx
inputs[18,indb,inda,0] = (inda+.5)*dy
inputs[20,:,:,:] = dx*dy*dz
return inputs
class SteadyRiemannSolution(object):
def __init__(self,pL,dL,ML,alphaL,pR,dR,MR,alphaR,gamma):
self.pL,self.dL,self.ML,self.alphaL = pL,dL,ML,alphaL
self.pR,self.dR,self.MR,self.alphaR = pR,dR,MR,alphaR
self.gamma = gamma
(self.pstar,self.alphastar,self.dstarL,self.dstarR,
self.MstarL,self.MstarR) = self.star_state()
if self.pstar/self.pL <= 1.:
self.left_wave = {
'type':'fan',
'head_angle':self.left_fan_angle(self.MstarL,self.alphastar),
'tail_angle':self.left_fan_angle(self.ML,self.alphaL)}
else:
self.left_wave = {
'type':'shock',
'shock_angle':self.left_shock_angle(
self.pstar,self.pL,self.alphaL,self.ML)}
if self.pstar/self.pR <=1.:
self.right_wave = {
'type':'fan',
'head_angle':self.right_fan_angle(self.MstarR,self.alphastar),
'tail_angle':self.right_fan_angle(self.MR,self.alphaR)}
else:
self.right_wave = {
'type':'shock',
'shock_angle':self.right_shock_angle(
self.pstar,self.pR,self.alphaR,self.MR)}
def __call__(self,x,y):
theta = np.arctan(y/x)
p,d,M,alpha = self.sample(theta)
a = (p/d*self.gamma)**.5
umag = M*a
u = umag*np.sin(alpha)
v = umag*np.cos(alpha)
return p,d,u,v
def sample(self,theta):
if theta <= np.pi*.5-self.alphastar: #Left of slip line
if self.left_wave['type'] == 'fan':
if theta <= self.left_wave['tail_angle']:
return self.pL,self.dL,self.ML,self.alphaL
else:
if theta >= self.left_wave['head_angle']: #Left star region
return self.pstar,self.dstarL,self.MstarL,self.alphastar
else: #Inside left fan
p_fan,alpha_fan,d_fan,M_fan = self.left_fan_state(
theta,self.pL,self.dL,self.ML,self.alphaL)
return p_fan,d_fan,M_fan,alpha_fan
else: #Left shock
if theta <= self.left_wave['shock_angle']:
return self.pL,self.dL,self.ML,self.alphaL
else:
return self.pstar,self.dstarL,self.MstarL,self.alphastar
else: #Right of slip line
if self.right_wave['type'] == 'fan':
if theta >= self.right_wave['tail_angle']:
return self.pR,self.dR,self.MR,self.alphaR
else:
if theta <= self.right_wave['head_angle']:
return self.pstar,self.dstarR,self.MstarR,self.alphastar
else:
p_fan,alpha_fan,d_fan,M_fan = self.right_fan_state(
theta,self.pR,self.dR,self.MR,self.alphaR)
return p_fan,d_fan,M_fan,alpha_fan
else: #Right shock
if theta >= self.right_wave['shock_angle']:
return self.pR,self.dR,self.MR,self.alphaR
else:
return self.pstar,self.dstarR,self.MstarR,self.alphastar
def Prandtl_Meyer(self,M):
out = (((self.gamma+1)/(self.gamma-1))**.5*
np.arctan(((self.gamma-1)/(self.gamma+1)*(M**2-1))**.5)
-np.arctan((M**2-1)**.5))
return out
def h_func(self,eta):
if eta <= 1.:
out = eta**(1./self.gamma)
else:
out = ((1+.5*(self.gamma+1)/self.gamma*(eta-1))/
(1+.5*(self.gamma-1)/self.gamma*(eta-1)))
return out
def g_func(self,eta,M0):
out = (2/(self.gamma-1)*(self.h_func(eta)/
eta*(1+.5*(self.gamma-1)*M0**2)-1))**.5
return out
def D_func(self,eta,M0):
out = (np.arcsin(1./self.g_func(eta,M0)*
(1+(self.gamma+1)/self.gamma*.5*(1./eta-1))**.5)
- np.arcsin(1./M0*(1+(self.gamma+1)/self.gamma*.5*(eta-1))**.5))
return out
def f_func(self,eta,M0):
if eta<=0.:
out = self.Prandtl_Meyer(self.gfunc(eta,M0))-self.Prandtl_Meyer(M0)
else:
out = self.D_func(eta,M0)
return out
def pressure_func(self,p):
return (self.f_func(p/self.pL,self.ML)+
self.f_func(p/self.pR,self.MR)+
self.alphaR-self.alphaL)
def pressure_guess(self):
return .5*(self.pL+self.pR)
def pressure_solve(self):
guess = self.pressure_guess()
return opt.newton(self.pressure_func,guess)
def star_state(self):
pstar = self.pressure_solve()
alphastar = self.f_func(pstar/self.pR,self.MR)+self.alphaR
dstarL = self.h_func(pstar/self.pL)*self.dL
dstarR = self.h_func(pstar/self.pR)*self.dR
MstarL = self.g_func(pstar/self.pL,self.ML)
MstarR = self.g_func(pstar/self.pR,self.MR)
return (pstar,alphastar,dstarL,dstarR,MstarL,MstarR)
def left_fan_state(self,theta,p,d,M,alpha):
return self.fan_state(theta,p,d,M,alpha,'left')
def right_fan_state(self,theta,p,d,M,alpha):
return self.fan_state(theta,p,d,M,alpha,'right')
def fan_state(self,theta,p,d,M,alpha,leftright_in):
leftright = {'left':-1,'right':1}
M_fan = opt.newton(self.fan_mach_func,M,args=(theta,M,alpha,leftright_in))
p_fan = p*opt.newton(self.fan_eta_func,p,args=(M_fan,M))
d_fan = d*(p_fan/p)**(1./self.gamma)
alpha_fan = alpha + leftright[leftright_in]*(
self.Prandtl_Meyer(M_fan)-self.Prandtl_Meyer(M))
return p_fan,alpha_fan,d_fan,M_fan
def fan_mach_func(self,M,theta,M0,alpha0,leftright_in):
leftright = {'left':-1,'right':1}
return (np.pi*.5-alpha0)-theta-leftright[leftright_in]*(
self.Prandtl_Meyer(M)-self.Prandtl_Meyer(M0)-np.arcsin(1./M))
def fan_eta_func(self,eta,M,M0):
return (2./(self.gamma-1)*(eta**((1-self.gamma)/self.gamma)*
(1+.5*(self.gamma-1)*M0**2)-1))**.5-M
def left_shock_angle(self,p,p0,alpha0,M0):
return np.pi*.5-alpha0-np.arcsin(((p/p0-1)*.5*(self.gamma+1)
/self.gamma+1)**.5/M0)
def right_shock_angle(self,p,p0,alpha0,M0):
return np.pi*.5-alpha0+np.arcsin(((p/p0-1)*.5*(self.gamma+1)/
self.gamma+1)**.5/M0)
def left_fan_angle(self,M,alpha):
return np.pi*.5-alpha-np.arcsin(1./M)
def right_fan_angle(self,M,alpha):
return np.pi*.5-alpha+np.arcsin(1./M)
if __name__=='__main__':
kwargs = {'pR':.25,'dR':.5,'MR':7,'alphaR':np.pi*.5,
'pL':1.,'dL':1.,'ML':2.4,'alphaL':np.pi*.5,
'gamma':1.4}
sol = SteadyRiemannSolution(**kwargs)
# import pdb;pdb.set_trace()
inputs = transonic_duct_inflow_generator()
# for inda in range(inputs.shape[1]):
# print inputs[5:15,inda,0]
import numpy as np
import matplotlib
# print matplotlib.__version__
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
def randrange(n, vmin, vmax):
return (vmax-vmin)*np.random.rand(n) + vmin
fig = plt.figure()
ax = Axes3D(fig)
n = 100
for i in range(inputs.shape[1]):
ax.scatter(inputs[17,i,:],inputs[18,i,:],inputs[19,i,:])
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.show()
print init.__doc__